1. Short introduction into rheology
Basics,
testing in rotation, creep and oscillation, extensional rheology

2. Contents
Viscosity Controlled shear rate (CR), shear stress (CS), deformation (CD)
Rotational testing - Newtonian and Non-Newtonian flow behavior - Yield stress - Thixotropy
Viscoelasticity Structural reasons, modeling
Creep & recovery testing - Description with Burgers model - Elastic and viscous share
Oscillatory testing - Time sweep e.g. relaxation, gelation, sedimentation - Amplitude sweep Linear viscoelastic range (LVR), stability - Frequency sweep liquid, paste-like or elastic? - Temperature sweep e.g. cross-linking - Cyclic testing stability
Extensional Rheology

3. Shear stress t, deformation g and shear rate g.
Sample height: h Deflection: x
Deformation: g
Shear stress t : force F applied to area A
Shear rate = change of deformation per time unit dt d g = . x A F h
Direction of force

4. Typical shear rates Application Shear rate (s-1)
Sedimentation
Phase separation
Leveling, running
Extrusion
Dip Coatings
Chewing
Pumping, stirring
Brushing
Spraying

5. Absolute and relative viscosity
"Resistance to flow"
Viscosity can be determined indirectly:
torque M * A factor .
shear stress
Viscosity = =
shear rate
rotational speed * M factor
Absolute viscosity readings with known measuring geometry only!

6. Relative viscosity
Any scale reading S (time, distance, angular deflection)
is set into ratio with a known viscosity standard
Viscosity of unknown material calculates as follows:
Parameters of testing (rotor, speed, filling …) strictly need to be
kept constant.
Calibration possible for Newtonian Liquids only!

7. Dynamic and kinematic viscosity
(Dynamic) viscosity h [Pas]
= shear stress [Pa]
= shear rate [1/s]
1 Pas = 1000 mPas
1 mPas = 1 cP (centi Poise)
Kinematic viscosity n [mm/s2]
= density [kg/m³]
1 mm/s² = 1 cSt (centi Stokes) .

8. Viscosity of fluids: Measured at 20°C
Substance
Viscosity
Water
1 mPas
Milk
mPas
Olive oil
100 mPas
Engine oil
1000 mPas
Honey
mPas
Bitumen
mPas

9. Measuring flow behaviour
Determination of flow behavior as a function of
varying shear stress or shear rate
Shear Stress  [Pa]
Shear Rate  [1/s]
Ramp (Thixotropy)
Steps (Steady state) .
Time t [s]

10. Newtonian flow behavior
Example: Oil
- Shear Stress
- Viscosity
 - Shear Rate . 5 10 15 20 25 30 35 40 45 50
Á [1/s]
100
150
200
250
300
350
400
450
500
‚ [Pa] 1
ƒ [Pa s]
Flow curve .
Viscosity curve

11. Shear thinning flow behavior: Structural reasons
Orientation Extension Deformation Dis-aggregation

12. Flow behavior: Flow curve
Linear plot
Newtonian
Pseudoplastic
(shear thinning)
Dilatant
(shear thickening)

13. Flow behavior: Viscosity curve
Double-logarithmic plot
Newtonian
Pseudoplastic
(shear thinning)
Dilatant
(shear thickening)

14. Yield stress 0 / yield point – a model
The yield stress 0 is the shear stress  required - to overcome elastic behavior and - obtain viscoelastic flow behavior
Shear stress 

15. Yield stress 0: Determination
Controlled deformation (CD) mode:
0: Maximum of the curve shear stress  vs. time t (linear scaling)
Controlled rate (CR) ramp:
0: Extrapolation of flow curve to shear rate  = 0 (linear scaling)
Controlled stress (CS) ramp:
0: Intersection of tangents in the change in slope of the curve log deformation  vs. log shear stress  .

16. Yield stress 0: Determination in CD-mode
Input: deformation  (constant)
Measurement: shear stress 
Result: shear stress  = f(time t)
Evaluation: Determination of the curve maximum (= yield stress 0)
0.5
1.0
1.5
2.0
2.5
Time t [min] 50
100
150
200
250
Shear Stress ‚ [Pa]
Curve discussion :
Method t [min] t0 [Pa]
Maximum

17. Yield stress 0: Determination in CR-mode
Input: shear rate  (varying)
Measurement: shear stress 
Result: shear stress  = f(shear rate )
Evaluation: yield stress 0 by Extrapolation of flow curve to shear rate  = 0 using a rheological model . 10 20 30 40 50 60
Á [1/s] 80
100
120
‚ [Pa]
Extrapolation
Casson: 0 = [Pa] . .

18. Yield stress 0: Determination in CS-mode
Input: shear stress  (increase logarithmic)
Measurement: deformation 
Result: log deformation  = f(log shear stress )
Evaluation : Transition between the linear regimes (= yield stress 0)
0.1
1.0
10.0
100.0
Shear Stress ‚ [Pa]
0.001
0.010
0.100
1.000
10.000
Deformation  [-]
0 = 16 Pa

19. Bingham flow behavior Example: Tooth paste
- Shear Stress
- Viscosity
 - Shear Rate . 5 10 15 20 25 30 35 40 45 50
Á [1/s]
100
150
200
250
300
350
400
450
500
550
‚ [Pa]
ƒ [Pa s]
Decrease in h due to yield stress
Flow curve .
Bingham yield stress:
‚¥ = 29 Pa
Viscosity curve

20. Thixotropy: Structural behavior
Time-dependent behavior: Primary particles
Agglomerates
Network

21. Thixotropy: Definition and determination
Definition of thixotropic flow behaviour:
- Decrease of viscosity as a function of time upon shearing, % recovery (= regaining the original structures) as a function of time without shearing.
Determination
(1) Time Curves
- Base-line of intact structure at low shear rate (e.g. CR mode: 1 1/s) or in oscillation (e.g. CD mode: 1% deformation) - Dis-aggregation at constant shear rate (e.g. CR mode: 100 1/s) - Re-aggregating time at low shear rate (e.g. CR mode: 1 1/s) or in oscillation (e.g. CD mode: 1% deformation)
(2) Flow Curves
- Ramp up, (peak hold,) ramp down at constant temperature. - The hysteresis area in this loop is a measure for the thixotropy.

22. Thixotropy: Time curve
Base-line, dis-aggregation, re-aggregating time

23. Thixotropy: Flow curve (thixotropy loop)
Input: shear rate 
- ramp up - (peak hold) - ramp down
Measurement: shear stress 
Result: viscosity  = f(shear rate , time t)
Evaluation: Determination of thixotropic loop area . 50
100
150
200
250
300
350
400
450
500
Shear Rate Á [1/s]
Shear Stress ‚ [Pa]
Thixotropic loop area .

24. Viscoelasticity: Structural reasons
Entanglement
in macromolecules
Structure/network
of an emulsion

25. How to model viscoelasticity?
Viscous flow
Elastic deformation
Spring
Dash pot .
  
Voigt/Kelvin- Model
  G*
Maxwell- Model
Burgers-Model

26. Testing methods for viscoelasticity
Method Input Information
Shear stress ramp Increasing shear stress Yieldpoint
Creep test Const. shear stress Deformation
Time curve Const. frequency and Monitoring of const. amplitude chemical reaction
Amplitude sweep Stepwise increasing Network stability amplitude
Frequency sweep Stepwise increasing Time frequency dependence
Temperature curve const. frequency and Temperature const. amplitude dependence

27. Signals applied by a rheometer. . .
(Stepped) Ramp (, ) Jump (, ) (Co-)Sinus (, ) Rotational Testing Creep & Recovery Oscillatory testing

28. Creep & recovery testing.
Shear rate g at low stress
Zero shear viscosity h0
Equilibrium compliance Je0
Ratio of viscous and elastic properties
Relaxation time l0
Elastic Modulus G0
Mostly elastic sample

29. Oscillatory testing: Principle
=0
(change of direction)
=0
(change of direction)

30. Oscillatory testing: Complex Quantities
Complex modulus G* = G’ + i G’’ (i2 = -1)
Storage modulus G’ (elastic properties)
Loss modulus G’’ (viscous/damping properties )
Loss angle d
Loss factor tand = G’’/G’
Complex Viscosity h*= G* / i w
Angular frequency w = 2p f G* G” d G’

31. Amplitude Sweep Material Stability
Example: Delicate gel
Material Stability
Gel strength correlates
with the gel's yield point
The critical stress from the stress sweep is used as characteristic value.
Remember the test is frequency dependent,
therefore it is a relative result!
LVR

32. Amplitude Sweep
Example: Gels with different carbopol (hydro colloid) content

33. Frequency Sweep: Frequency and temperature dependence
elastic
paste
flowing

34. Frequency Sweep Cross-over Material Characterization
Paste - Entangled solution (circles)
Gel - 3D network
(triangles)
Note:
A Gel is not necessarily
“stronger” than a Paste

35. Time Sweep: Gelation Parameters: f = 0.5 Hz g = 1 % T = 35°C
Verlustanteile G"
Cross-Over
Parameters:
f = 0.5 Hz
g = 1 %
T = 35°C

36. Curing
Storage modulus G’ Loss modulus G”

37. Test for prediction of temperature stability Brummer et al
Oscillation (g , w = const.)
Cyclic temperature ramps ( °C, 20 min each)
Indicators: G' und G":
- G' and G" not affected sample is stable
- Changes in G' and G" sample not stable

38. Test for prediction of temperature stability Brummer et al
Example: Cosmetics
G´´ [Pa] G´ [Pa]
Temp. T [°C]
w = konstant
Time t [min]
Cyclic testing  stable sample

39. Test for prediction of temperature stability Brummer et al
Example: Cosmetics
G´´ [Pa] G´ [Pa]
Temp. T [°C]
w = konstant
Time t [min]
Cyclic testing  sample not stable

40. Extensional Rheology
HAAKE CaBER 1 - Capillary Breakup Extensional Rheometer - Designed for fluids
Extensional behaviour ist relevant for - Processability - Strand formation / stringiness - Time to breakup - Relaxation time - Filling of bottels etc.

41. Extensional Rheology: HAAKE CaBER 1 - how it works
Sample
Apparent viscosity
Laser micrometer
Calculations
Result: Apparent extensional viscosity vs.
Hencky strain
Measurement D=f(t)

42. Extensional Rheology: Bottle Filling
Subtle changes in shampoo formulation caused difference in strand detachment during bottle filling
Up-line characterization would prevent costly external washing of poorly-filled bottles

43. Further Reading
A handbook of elementary rheology. H.A. Barnes, University of Wales, Aberystwyth, Dyfed, U.K., 2000
Non-Newtonian flow in the process industries - fundamentals and engineering applications. Chhabra RP, Richardson JF, Butterworth Heinemann, Oxford, 1999
A practical approach to rheology und rheometry G. Schramm, Thermo Haake GmbH, Karlsruhe, 1995
Engineering rheology - Oxford engineering science series vol 52. R.I. Tanner, Oxford University Press, Oxford, 2000

44. Questions ? 2